Determine the exact and ordinary interest on ₱16,900 at 14% from January 07, 2023, to June 10, 2023
using actual and approximate time.

To determine the **exact interest** and **ordinary interest** on ₱16,900 at 14% from January 7, 2023, to June 10, 2023, we'll follow these steps:

### Given:
- Principal (\( P \)) = ₱16,900
- Rate (\( r \)) = 14% = 0.14
- Time period: January 7, 2023, to June 10, 2023

We'll compute interest based on two methods:
1. **Exact interest**: Using actual days in the year (365 days).
2. **Ordinary interest**: Using 360 days in the year.

### Step 1: Determine the time period
To find the time period, we count the actual number of days between January 7, 2023, and June 10, 2023.

- January 7 to January 31 = 24 days
- February (non-leap year) = 28 days
- March = 31 days
- April = 30 days
- May = 31 days
- June 1 to June 10 = 10 days

**Total days** = 24 + 28 + 31 + 30 + 31 + 10 = **154 days**

### Step 2: Compute the interest
#### (a) **Exact interest** formula:

\[
\text{Exact Interest} = P \times r \times \frac{t}{365}
\]

Where:
- \( P = 16,900 \) (principal)
- \( r = 0.14 \) (rate)
- \( t = 154 \) days (actual time)

\[
\text{Exact Interest} = 16,900 \times 0.14 \times \frac{154}{365}
\]

#### (b) **Ordinary interest** formula:

\[
\text{Ordinary Interest} = P \times r \times \frac{t}{360}
\]

Where:
- \( t = 154 \) days (same time period, but calculated over a 360-day year)

\[
\text{Ordinary Interest} = 16,900 \times 0.14 \times \frac{154}{360}
\]

Let's calculate the values.### Results:
- **Exact Interest**: ₱998.26
- **Ordinary Interest**: ₱1,012.12

These are the interests calculated over the period from January 7, 2023, to June 10, 2023.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How does the interest calculation differ in a leap year?
2. What is the impact of different compounding frequencies on interest?
3. How does the interest rate affect the final interest amount over the same period?
4. What are the key differences between exact and ordinary interest in financial calculations?
5. How would the interest change if calculated for a longer period, say 12 months?

**Tip**: Ordinary interest is often used for simplified banking calculations, while exact interest gives more precision based on actual days in a year.

Determine the exact and ordinary interest on ₱16,900 at 14% from January 07, 2023, to June 10, 2023 using actual and approximate time.

Learn how to determine the exact and ordinary interest on ₱16,900 at 14% over the period from January 7, 2023, to June 10, 2023. Understand the difference between exact and ordinary interest, with detailed calculations using financial mathematics. Suitable for students in Grades 9-12.

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